LONDON - Prince William's wife Kate gave birth to a boy on Monday, the couple's first child and the third in line to the British throne, heralding celebrations in London and messages of goodwill from across the world."We could not be happier," Prince William said in a brief statement, after he witnessed the birth of his son at 4:24 p.m. (1524 GMT), an event that sparked an international media frenzy and the illumination of London landmarks in blue.FrenzyThe royal birth has provoked a similar frenzy, with media keeping up a deluge of speculative reports for days beforehand and particularly throughout Monday."Right across the country and indeed right across the Commonwealth people will be celebrating and wishing the royal couple well," Prime Minister David Cameron told waiting reporters in Downing Street."It is an important moment in the life of our nation but I suppose above all it's a wonderful moment for a warm and loving couple who got a brand new baby boy."Outside Buckingham Palace, there was a party atmosphere with well-wishers laying flowers and teddy bears, singing "God Save the Queen" and "Happy Birthday", and children waving flags."The build up to the birth has been so big I'm just happy it's finally come. I'm pleased it's a boy, you always want a boy really," said Alice Durrans, who rushed from a nearby restaurant after hearing the news.Deborah Beeson, a banker from the United States, was ecstatic."It's wonderful. I got chills. I cried," she said. "You know America loves Kate. She's just beautiful, she has dignity."There will be a 41-gun salute at London's Hyde Park and 62 rounds fired at the Tower of London on Tuesday to herald news of the birth.The baby arrives at a time when the royal family is riding a wave of popularity. An Ipsos Mori poll last week showed 77 percent of Britons were in favor of remaining a monarchy over a republic, close to its best-ever level of support.Dark daysThe dark days for the House of Windsor after the death of William's mother Princess Diana in 1997, which led to public anger at the royals, have been replaced with outpourings of support for William and Kate's wedding and the Diamond Jubilee for the queen last summer."It's been a remarkable few years for our royal family," Cameron said.The couple, who have been living in a cottage in north Wales where William is based as a Royal Air Force helicopter pilot, will eventually take up residence with their baby at Apartment 1A at London's Kensington Palace when a 1 million pound refurbishment is completed later this year.The palace was also William's childhood home.The young royal couple have become global stars after some 2 billion people tuned in to watch their glittering marriage ceremony in 2011, while Kate is seen as a fashion icon. JPost.com contributed to this report.His office said Kate and the baby, weighing 8 lbs 6 oz (3.8 kg) and to be publicly named at a later date, were both doing well and would stay in hospital overnight.Prince William phoned his grandmother the queen to give her the news, and also contacted his father Prince Charles and brother Prince Harry, all of whom were said to be delighted. The addition to the family is third in line to the throne after Prince Charles and William.It might take some time for the name to emerge however. The announcement of William's name took more than a week, but bookmakers make George the favorite, followed by James.As the birth of the queen's third great-grandchild was announced, a loud cheer went up from the well-wishers and media gathered outside St. Mary's Hospital in west London, where William was also born to the late Princess Diana in 1982."It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy," said Prince Charles, the heir to the throne.Within minutes, messages of congratulations began flooding in, while crowds gathered outside the queen's London residence Buckingham Palace where an official notice was placed on a gold-colored easel at the main gates.US President Barack Obama was one of the first world leaders to welcome the birth."Michelle and I are so pleased to congratulate The Duke and Duchess of Cambridge on the joyous occasion of the birth of their first child," he said. "We wish them all the happiness and blessings parenthood brings."Prime Minister Binyamin Netanyahu was also quick to send his congratulations on Monday night."The citizens of Israel send their warmest wishes to Her Majesty Queen Elizabeth II, Prince Charles, the Royal Family and all residents of the United Kingdom," the prime minister wrote in a message on his Facebook page.The royal couple, officially known as the Duke and Duchess of Cambridge, had arrived at the hospital shortly before 6 a.m. and entered through a back door to avoid massed ranks of British and international media camped outside the main entrance.Kate and William, both aged 31, met when they were students at St. Andrews University and were married in April 2011 in a spectacular wedding broadcast around the world.